Temperature dependence of association constant, extinction coefficient and total absorption...

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Spectrochlmica Acta, 1967 Vol. 2SA, pp. 2057 to 2042. Pergamon Preu Ltd. Printed In Northern Ireland Temperature dependence of association constant, extinction coefficient and total absorption intensity of an organic charge-transfer complex R. FOSTER and I. B. C. MATHESON Chemistry Department, Queen's College, University of St. Andrews, Dundee, Scotland (Received 1 November 1966) Abstract--Determinations of association constant, extinction coefficient and total absorption intensity for the system hexamethylbenzene- tetracyanoethylene in 1,2-dichloroethane have been made over a temperature range of 45 °. The extinction coefficient of the complex decreases slightly with increasing temperature whilst the total absorption intensity remains constant. The observations are consistent with the postulate that, under the conditions used, a single 1 : 1 complex species is formed with no significant contributions from isomeric complexes, or from contact charge transfer. INTRODUCTION ELECTRON donors (D) and electron acceptors (A) may interact in solution to form a charge-transfer complex [1]. The complex is usually characterised by an absorption band, or bands, not present in either component. This absorption has been assigned to an intermolecular charge transfer transition(s) [1]. The intensity of the band(s) has been taken as a measure of the concentration of the complex. If it is assumed that only a 1:1 complex DA is formed then an association constant K~ may be defined as K~ = [DA]/[D][A] (1) Many algebraic methods have been used to evaluate Ko and e (the molar extinction coefficient(s) of DA) from values of the total concentrations (free and eomplexed) [A]0 and [D]o of A and D respectively and measurements of optical density (d) due to the absorption by the complex [2]. Some of the results which have been obtained are anomalous [2]. Various explanations have been suggested, for example the presence oftermolecular complexes [3], specific solvation [4] and the apparent disobedience of Beer's law by the complex species [2]. Whatever the cause of these anomalies, the most consistent results from optical data are obtained when [A]0 ~ [D]o, and when the degree of association is fairly high [2, 4]. However, even under the condition [A]0 ~ [D]0 the possibility, envisaged by [1] R. S. M~I~, J. Am. Chem. Soe. ~, 600 (1950); J. Phys. Chem. 56, 801 (1952); J. Am. Chem. Soe. 74, 811 (1952). [2] See for example: P. H. EMSLIV.,R. FOSTER, C. A. F~'~. and I. HoRn, Tetrahedron 21, 2843 (1965). [3] S. D. Ross and M. M. L~ES, J. Am. Chem. Soe. 79, 76 (1957); G. D. JOH~rSO~ and R. E. BowE~¢, ibid. 87, 1655 (1965). [4] S. CA~TER, J. N. MUgRET.T. and E. J. Rosc~, J. Chem. Soc. 2048 (1965). 2037

Transcript of Temperature dependence of association constant, extinction coefficient and total absorption...

Spectrochlmica Acta, 1967 Vol. 2SA, pp. 2057 to 2042. Pergamon P r e u Ltd. Pr inted In Northern Ireland

Temperature dependence of association constant, extinction coefficient and total absorption intensity of an organic

charge-transfer complex

R. FOSTER and I. B. C. MATHESON

Chemistry Department, Queen's College, University of St. Andrews, Dundee, Scotland

(Received 1 November 1966)

Abstract--Determinations of association constant, extinction coefficient and total absorption intensity for the system hexamethylbenzene- tetracyanoethylene in 1,2-dichloroethane have been made over a temperature range of 45 °. The extinction coefficient of the complex decreases slightly with increasing temperature whilst the total absorption intensity remains constant. The observations are consistent with the postulate that, under the conditions used, a single 1 : 1 complex species is formed with no significant contributions from isomeric complexes, or from contact charge transfer.

INTRODUCTION

ELECTRON donors (D) and electron acceptors (A) m a y in te rac t in solut ion to form a charge- t ransfer complex [1]. The complex is usual ly character ised b y an absorpt ion band, or bands, no t present in e i ther component . This absorp t ion has been assigned to an in termolecular charge t ransfer transit ion(s) [1]. The in tens i ty of the band(s) has been t aken as a measure of the concent ra t ion of the complex. I f i t is assumed t h a t only a 1:1 complex D A is fo rmed t hen an association cons tant K~ m a y be defined as

K~ = [DA] / [D][A] (1)

Many algebraic methods have been used to eva lua te Ko and e (the molar ex t inc t ion coefficient(s) of D A ) f rom values of the to ta l concentra t ions (free and eomplexed) [A]0 and [D]o of A and D respect ively and measurements of optical dens i ty (d) due to the absorp t ion by the complex [2].

Some of the results which have been ob ta ined are anomalous [2]. Various explanat ions have been suggested, for example the presence of te rmolecula r complexes [3], specific solvat ion [4] and the appa ren t disobedience of Beer 's law b y the complex species [2]. W h a t e v e r the cause of these anomalies, the most consistent results f rom optical da t a are ob ta ined when [A]0 ~ [D]o, and when the degree of association is fair ly high [2, 4].

However , even unde r the condit ion [A]0 ~ [D]0 the possibility, envisaged b y

[1] R. S. M ~ I ~ , J . Am. Chem. Soe. ~ , 600 (1950); J . Phys. Chem. 56, 801 (1952); J. Am. Chem. Soe. 74, 811 (1952).

[2] See for example: P. H. EMSLIV., R. FOSTER, C. A. F~'~. and I. H o R n , Tetrahedron 21, 2843 (1965).

[3] S. D. Ross and M. M. L~ES, J. Am. Chem. Soe. 79, 76 (1957); G. D. JOH~rSO~ and R. E. BowE~¢, ibid. 87, 1655 (1965).

[4] S. CA~TER, J. N. MUgRET.T. and E. J. Rosc~, J. Chem. Soc. 2048 (1965). 2037

2038 R. FOSTER and I. B. C. MATHESON

ORGEL and MULLIKEN [5], of isomeric 1:1 charge transfer complexes and 1:1 contact pairs still exists. The following work was carried out in order to test for the presence of either of these perturbing influences on the observed optical absorption in a given system.

Hexamethylbcnzene-tetracyanoethylene in 1,2-dichloroethane was chosen for the following reasons: (a) the charge-transfer absorption maximum at 540 m/~ is a single band well separated from the absorptions of the component molecules; (b) the association constant is known to be reasonably large ; (c) the solvent will dissolve a sufficient quanti ty of tetracyanoethylene to permit solutions with [A]0 ~ [D]o to be used.

EXPERIMENTAL Mater ia l s

1,2-Dichloroethane was washed with dilute aqueous potassium hydroxide, then with water; dried over, and distilled from, phosphoric oxide. I t was finally frac- tionated, b.p. 83.5°/760 mm. Tetracyanoethylene was recrystallized from benzene as the benzene complex. The benzene was then pumped off and the tetracyanoethylene twice sublimed, m.p. 198-200 °. Hexamethylbenzene was prepared by the method of CULLI~AN]~ et al. [6]. I t was recrystallized five times from ethanol and twice sublimed, m.p. 165-165.5 °.

A n a l y t i c a l

Optical density measurements were made using a manually-operated Optica CF4 Spectrophotometer. The optical density calibration was checked using standard potassium chromate-potassium hydroxide solutions. The technique for measuring the solutions has been described [7]. The temperature of the solutions was controlled to within +0.05 ° by circulating water or aqueous ethylene glycol through a specially constructed cuvette jacket. Appropriate corrections were made for the effect of solvent expansion on the concentrations of the various species present.

For solutions where [D]0 ~ [A]0 let:

[D]0 = n[A] 0 (2)

I f the measured absorption is corrected for the small absorption due to the free D, A and the solvent then:

d = [ D A ] . l (3)

where l is the path length in cm of the optical cuvette. From equations 1, 2 and 3 it may be shown that [8]:

l[A]o ( n + l ) ] ] 1 - - - - - - + . (4)

d n e n K c e [A]o

The plot of [A]o/d against [A]0 -1 should be linear. From the gradient and the intercept with the ordinate, Kc and e may be evaluated.

[5] L. E. ORGEL and R. S. MtmLIKE~r, J. Am. Chem. Soc. 79, 4839 (1957). [6] N. ~. CIYLLIZ~ANE, S. J. CTrAXD and C. W. C. DAw~u~s, Org. Syn. 35, 73 (1955). [7] R. FOSTER, J. Chem. Soc. 1075 (1960). [8] cf. Ref. [3], also R. FOSTER, d. Chem. Soc. 5098 (1957).

Temperature dependence of association constant of an organic charge-transfer complex 2039

A min imum of t h i r t y points was used in an y single de terminat ion . The best s t ra igh t line was ob ta ined b y the least squares method. E v e r y de te rmina t ion was repea ted at least once.

F o r band measurements , the ex t inc t ion coefficients p lo t ted against f requency and the ba nd wi th (A~) a t ha l f the m a x i m u m band height was measured. The band area was es t imated b y assuming a Gaussian shape so t h a t the to ta l in tens i ty (A) = 1-0645 ~. A~. F r o m this value, the oscillator s t rength (f) was calculated using the relat ionship [9]:

f : 4.319 × 10 - g l ' e . d ~ (5)

where i t is assumed t h a t A = S e dr . In equa t ion 5, e is measured in 1.mole -1 cm -1 and ~ is measured in cm -1.

RESULTS

Values of /£c and ~ ob ta ined f rom plots of [A]o/d against [A]o -1 using equa t ion 4 are summar ized in Table 1. Plots of logx0K~, log10 (Kc~) and loglo e against T -1 (where T is the t empe ra tu r e in °K) are given in Fig. 1. The gradient of the

Table 1. Calculated values for K c, Kce and e for the complex between hexamethyl- benzene and tetracyanoethylene in 1,2-dichloroethane at various temperatures

Temp. Kv Kce e (°G) (1. mole -1) (1.~ molo -2 cm -1 × 10 -4) (I. molo --1 cm -1 × 10 -a)

--3.90 46-53 17.660 3.79~ 3.40 35.54 13.287 3.739

11.45 26.75 9"795 3.675 19-45 20-4 s 7.463 3.645 27.45 15.9~ 6.893 3.69 o 33-70 13.11 4-773 3.641 41.00 10.98 3.915 3.57 o

first plot gives AH = --5.4 e kca l . mole -1. F r o m the plot of lOglo (/£~e) AH = - -5 .64 kc a l . mole - i , AS = 12.6 e.u., AG298o = --1.69 k ca l . mole -I, TAS29so ~- - - 3 . 7 7 kca l . mole -1 (for s t anda rd s ta te of 1 mo le . 1-1).

The spec t rum of the charge t r a n s f e r band for a given solutions corrected for absorp t ion by the components and b y the solvent is shown in Fig. 2. The absorp t ion band intensit ies are summar ized in Table 2. A n y shift in 2max----540 m/~ wi th t e m p e r a t u r e is too small to be measured over the range --3.9 ° to -}-41.0 ° .

DISCUSSION

ORGEL and MULTX~EN [5] have discussed the possibil i ty of the optical absorpt ion of an organic donor - accep to r sys tem being affected b y complex isomerism and con tac t charge t ransfer . T h e y define t rue complex format ion as being the s i tuat ion where the numbe r of 1 : 1 D A pairs exceeds the n u m b er which m a y be expec ted on

[9] C. SAI~DORFY, Electronic Spectra and Quantum Chemistry, p. 105. Prentice-Hall (1959).

2040

1"8 F

I "

1.6

1.4

1.2

I-C

o . s ~ 5-5 5 5

T~l (OK' lx i0 3)

Fig. 1. Plots of (A) logzoKc; (B) logx0(Kc~); (C) logz0¢ against the reciprocal of the absolute temperature for the complex hexamethylben- zene-tetracyanoethylene in 1,2-diehloroethane.

R. FosT~,~ and I. B. C. MATS~,SON

- - 5"4 4¢"-

-- 5 2 A

g

- - 5"0

7 x

- 4 . 8

3 '59

5,58 w

5.57 o

- - 3 . 5 6 _~

- - 3.55

- - 3.54 _L____ 5.7 12 14 16 18 20 22 24 26

v, cm -~ x 10 -5

Fig. 2. The charge-transfer absorption spectrum of the complex hexamethylben- zene-tctracyanoethylcne in 1,2-diehloro- ethane, corrected for the absorption by the components and the solvent, at --3.9°C.

Table 2. Variation of extinction coefficient (e), band width at half maximum intensity (Av) and oscillator strength (t) of the charge-transfer band with temperature

Temp. • Av (°C) (1.mole -1 cm -1) × 10 -a (cm -1) × 10 -a i

-3 .90 3.79~ 5.15 0.0844 3.40 3.739 5.25 0.0848

11.45 3.675 5-26 0-0835 19.45 3.645 5.35 0.0842 27.45 3.690 5.34 0.0851 33.70 3.641 5.36 0.0843 41.00 3.57 o 5-50 0.0848

the basis of r a n d o m encounters . The excess is the n u m b e r of t rue complexed pairs present . T h e y suggest t h a t i t is possible t h a t in the case of r a n d o m contac ts the over lap in tegra l of the a p p r o p r i a t e donor and accep t e r orbi ta ls is appreciable . This gives rise to opt ical a b s 0 r p t i o n - - a process which t h e y t e r m contac t charge t ransfer . Complex i somer ism refers to the s i tua t ion where more t h a n one t rue charge t rans fe r complexes of different geometr ic configurat ions are present .

Tempera ture dependence of association constant of an organic charge-transfer complex 2041

ORGEL and MUH,TKEN [5] also showed tha t for the case of the presence of several isomeric complexes, the normal type of B~.~.SI--I-hLDEBRAND [10] evaluation of Kc, where [D]0 >> [A]o, will give:

'K c (measured) = ~ K~ (6)

(measured) = ~ K~/ZK~ (7)

where K~ and s~ are the values of Kc and ~ respectively for the i-th 1 : 1 complex between A and D.

For contact charge transfer in a given system, ORGEL and MVLLrKE~" [5] derived the relationship

e measured = e(1 + K ~ ) (8)

where C = constant. More recently I~UE [11] has pointed out tha t random collisions will themselves lead to a finite association constant.

Determinations of K~ (and e) will consequently not demonstrate the presence or absence of isomeric complexes or contact charge-transfer, although if they are present the values of K~ and e obtained will be incorrect. However, unless AH for the formation of the different 1 : 1 complexes is identical, plots of log10 K vs. T -1 should be non-linear, i.e. AH (measured) should be temperature dependent, likewise if isomeric 1 : 1 complexes and/or contact charge transfer are present, the intensity of the charge transfer band should be temperature dependent [5].

For the system studied there is no evidence for a deviation from linearity of the plot of lOglo Ko vs. T -1 over a 45 ° temperature range (Fig. 1). This suggests tha t only one 1:1 complex is present under the experimental conditions employed. Because of the only slight variation of e with temperatures, a plot of log10 (Kce) yields a straight line with effectively the same slope (Fig. 1). This is of importance in experimental determinations of AH. There is much doubt concerning the validity of many results obtained f o r / ~ from optical data using the condition [D]0 >> [A]0. However, several groups of workers [2-4] are agreed that from such determinations the product K~e may be estimated with reasonable certainty, (though for very different reasons). The present results suggest that the temperature variation of this product K~e may yield good estimates of AH.

The value of E shows in fact a slight decrease with increasing temperature (Fig. 1). This is entirely accounted for by the temperature band-broadening and is reflected in the temperatures independence of the oscillator strength f. This latter observation confirms the conclusion that no isomeric 1:1 complexes are present and it suggests that contact charge transfer is also insignificant. The only published value of f for this complex [12]; namely f = 0.18 is at variance with the present value (f = 0.084). Although former value is based on an extinction coefficient obtained from a Benesi-Hildebrand type of analysis which, as stated above, yields

[10] H. A. BENESI and J. H. HILDEBRAI~D, J. Am. Chem. Soc. 71, 2703 (1949). [11] J. E. PRUE, J. Chem. Soc. 7534 (1965). [12] G. BRIEGL~.B, Electr°nen'D°nat°r-Accept°r'K°mplexe' p. 62. Springer (1961).

2042 R. FOSTER and I. B. C. MATHESON

doubtfully separa ted values of e and Ko, nevertheless the difference between the two values of f appears to be too large to be completely explained in this way.

Although in the present work for the system studied under the conditions used, no evidence for isomeric 1:1 complexing or for contact charge-transfer has been obtained, this cannot in itself be taken to show that such behaviour cannot occur in other electron donor-electron acceptor systems.

Acknowledgement--The Authors are grateful to the Science Research Council for a grant (to I. B. C.M.).